Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T7/00—Image analysis
  • G06T7/0002—Inspection of images, e.g. flaw detection
  • G06T7/0004—Industrial image inspection
  • G06T7/001—Industrial image inspection using an image reference approach
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
  • G01N23/20—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials
  • G01N23/203—Measuring back scattering
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
  • G01N23/22—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material
  • G01N23/225—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material using electron or ion
  • G01N23/2251—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material using electron or ion using incident electron beams, e.g. scanning electron microscopy [SEM]
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T5/00—Image enhancement or restoration
  • G06T5/50—Image enhancement or restoration using two or more images, e.g. averaging or subtraction
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T5/00—Image enhancement or restoration
  • G06T5/70—Denoising; Smoothing
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N2223/00—Investigating materials by wave or particle radiation
  • G01N2223/05—Investigating materials by wave or particle radiation by diffraction, scatter or reflection
  • G01N2223/056—Investigating materials by wave or particle radiation by diffraction, scatter or reflection diffraction
  • G01N2223/0566—Investigating materials by wave or particle radiation by diffraction, scatter or reflection diffraction analysing diffraction pattern
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N2223/00—Investigating materials by wave or particle radiation
  • G01N2223/60—Specific applications or type of materials
  • G01N2223/606—Specific applications or type of materials texture
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N2223/00—Investigating materials by wave or particle radiation
  • G01N2223/60—Specific applications or type of materials
  • G01N2223/607—Specific applications or type of materials strain
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T2207/00—Indexing scheme for image analysis or image enhancement
  • G06T2207/10—Image acquisition modality
  • G06T2207/10056—Microscopic image
  • G06T2207/10061—Microscopic image from scanning electron microscope

Definitions

• the invention relates to an image processing method obtained by diffraction detector.
• the field of application of the invention relates to the analysis of crystalline or polycrystalline materials, and in particular backscattered diffraction analysis in high resolution (in English: HR-EBSD for High Resolution Electron Backscatter Diffraction).
• the detector may be an electron diffraction detector producing electron diffraction figures, called Kikuchi figures, the analysis of which makes it possible to calculate very precisely the (relative) variations of the crystal lattice parameters.
• Each thumbnail provides an average inter-correlation displacement.
• the size of the thumbnail must be large to contain a sufficient number of Kikuchi strips.
• these overlaps introduce strong spatial correlations between thumbnails so that the increase in the number of thumbnails, starting from a certain threshold, makes it possible neither to reduce the measurement uncertainty, nor to reduce bias. systematic.
• the choice of positioning of the imagettes influences the results obtained, which is a manifestation of the non-optimality of the method used. In case of relatively large deformations, significant rotations of the patterns can be observed, greater than one degree.
• the object of the invention is to provide a method and an image processing device which alleviate the drawbacks of the state of the art by allowing the calculation of the displacement field between the images, with a better quality and a cost. lower calculation.
• a first object of the invention is a method of image processing, obtained by a diffraction detector, of a crystalline or polycrystalline material, in which the detector measures:
• a displacement field for moving pixels of the first image to pixels of a deformed image, according to:
• the current elastic deformation gradient tensor is made to take a determined value of the elastic deformation gradient tensor.
• the current displacement field is calculated from the current elastic deformation gradient tensor and the pixel coordinates of the first image.
• third digital pixel values of a distorted image are calculated by correcting the second image at the pixel coordinates to which the current displacement field has been added.
• the distorted image is corrected from the current displacement field, and is called the third corrected image or image corrected having third pixel values, to distinguish it from the first and second images.
• the diffraction detector notably makes it possible to measure a reference configuration of the diffraction geometry, associating with the coordinates of each pixel, a direction of the beam diffracted electronics, whose origin corresponds to the normal projection in the image plane of the detector, the source point of the beam diffracted in the material,
• a first diffraction pattern (of Kikuchi) of the material being in a reference state giving a so-called reference image, ie a grayscale image whose numerical value corresponds in each pixel to a density of electrons diffracted in the direction geometrically connected to the position of the pixel,
• this second image giving second digital values of gray levels at each pixel.
• the displacement field is defined in each pixel, to match the pixels of the first diffraction image to the pixels of the diffraction image of the deformed crystal, so as to coincide as much as possible with the gray levels of the paired pixels, this displacement field being thus associated with a direction of the diffracted beam and taking an algebraic form whose expression is a known function of the elastic deformation gradient tensor.
• the current elastic strain gradient tensor is initialized to a predetermined value of tensor and is updated during the iterations.
• the third digital pixel values of the third deformed image are calculated by interpolating the second image to the pixel coordinates to which the field of view has been added. current displacement.
• the third pixel values of a distorted image are provided, which are a correction of the second image, based on a major part of the image, in a shorter time.
• the calculation provided by the invention further reduces the measurement uncertainty of the displacement field between the first image and the second image.
• the invention is thus specially adapted, in embodiments, to calculating from the third image, a deformation of the material between the first image and the second image.
• the tensor F elastic deformation gradient is equal to where F 1 , F 2 , F 3 , F 4 , F 5 , F 6 , F 7 , F are the components of the tensor
• the displacement field, u x , u y for moving pixels of the first image to pixels of a deformed image, depending on:
• predetermined coordinates x *, y *, z * of the center corresponding to the normal projection, in the image plane of the detector, of the source point of the beam diffracted in the material
• the iterative algorithm is performed by a Gauss-Newton type method.
• a correction vector F F J satisfying the equation is calculated.
• [M] is a Hessian matrix of dimension 8 x 8, having as coefficients
• / represents the first pixel values of the first image
• x represents the two coordinates (x, y) of pixels
• x represents the two coordinates (x, y) of pixels
• ⁇ y ⁇ is the residue vector with components
• the tensor F elastic deformation gradient has, as components F ⁇ r eight components , F, F 5, F 6, F j, F ⁇ e t a ninth component set at 1, namely according to the following equation:
• the image processing method is executed for the greater part or for all the pixels of the first image and the second image.
• the first and second images are obtained after filtering overexposed pixel values by replacing them with an average of neighboring pixels thereof.
• Aberrant values are thus filtered (noise conventionally defined as "salt and pepper” which occurs for certain detectors).
• the first and second images are obtained after filtering the pixel values by subtraction of overall gray level trends, represented by a second or third order polynomial obtained by a regression process.
• the first and second images are obtained after filtering the pixel values by a Gaussian smoothing filter.
• the image processing method is executed for several second images. According to one embodiment of the invention, at least one of:
• a residual calculated as the difference between, on the one hand, the third digital pixel values of the corrected deformed image, having been calculated for the corresponding displacement field as fulfilling the convergence criterion on the determined value of the gradient tensor; elastic deformation, and secondly the first numerical values of pixels of the first image,
• the first and second images are obtained after subtraction of a background image.
• a second object of the invention is an image processing device of a crystalline or polycrystalline material, comprising a diffraction detector making it possible to acquire:
• the device comprises at least one less a calculator, comprising at least one memory, in which is recorded a field of displacement, for moving pixels of the first image to pixels of a distorted image, based on:
• the computer being configured for
• calculating third digital pixel values of a distorted image by applying the second image to the pixel coordinates to which the current displacement field has been added, during an iterative algorithm, performing iterations of the first, second and third calculation steps on reactualized tensor constant values, to satisfy a convergence criterion on the determined value of the elastic strain gradient tensor, in order to calculate the corresponding displacement field.
• a third object of the invention is a computer program, comprising code instructions for implementing the image processing method of a crystalline or polycrystalline material as described above, when it is executed on a calculator.
• FIG. 1 schematically represents an image acquisition and processing device according to one embodiment of the invention
• FIG. 2 diagrammatically shows in perspective the projection of the diffracted beams by an image processing device according to one embodiment of the invention as well as the effect produced by the elastic deformation gradient tensor on the difffacted beam
• FIG. 3 diagrammatically shows in side view the projection of the beams diffracted by an image processing device according to one embodiment of the invention
• FIG. 4 schematically represents a flowchart of the image processing method according to one embodiment of the invention
• FIG. 5A shows an image of a specimen, taken by a scanning electron microscope
• FIG. 5B shows an image obtained from FIG. 5A by software of the state of the art
• FIG. 5C shows a color scale of FIG. 5B
• FIGS. 6A and 6B show an example of diffraction starting images of a specimen
• FIG. 6C represents the difference obtained between the images of FIGS. 6A and 6B
• FIG. 6D represents a value calculated for an elastic deformation gradient tensor appearing in the method and the image processing device according to one embodiment of the invention, in the example of FIGS. 6A and 6B,
• FIGS. 6E, 6F, 6G, 6H and 61 represent images appearing in different steps of the method and of the image processing device according to embodiments of the invention, in the example of FIGS. 6A and 6B,
• FIGS. 7A, 7B, 7C, 7D and 7E represent components of a stress tensor obtained by the method and the image processing device according to embodiments of the invention, starting from FIG. 5A,
• FIG. 8A shows a von Mises equivalent stress obtained by the method and the image processing device according to embodiments. of the invention, from FIG. 5A, and FIG. 8B represents a histogram of this constraint.
• a diffraction detector 10 or sensor 10 or camera 10
• clichés of a CR crystalline or polycrystalline material.
• the detector 10 may be a high-resolution backscattered diffraction detector, called EBSD or HR-EBSD (High Resolution Electron Back-Scattered Diffraction (HR-EBSD)).
• HR-EBSD High Resolution Electron Back-Scattered Diffraction
• HR-EBSD High Resolution Electron Back-Scattered Diffraction
• the detector 10 measures a first image / CR material in a reference state, giving first numerical values flx, y) of pixels (for example gray levels or other) as a function of the two coordinates x, y pixels.
• the EBSD detector also measures one or more second image (s) of material CR in a state that is deformed with respect to the reference state.
• the second image g gives second pixel numerical values g (x, y) (for example, gray levels) as a function of the two x, y coordinates of the pixels.
• the images / and g are chosen during step E2 of FIG. 4. In FIGS. 2 and 3, the 3 x, y and z directions are orthonormal to one another.
• the deformed state and the reference state are obtained by applying different mechanical stresses to the material CR, for example by applying no mechanical stress to the material CR in the reference state. and applying a determined mechanical stress to the material CR in the deformed state.
• means may be provided for exerting and / or controlling a mechanical stress on the CR material.
• the detector 10 is part of a measuring device 1 comprising an internal source 2 for emitting a beam 3 of incident particles and the detector 10 for backscattered diffraction.
• the source 2 and the beam 3 of incident particles are positioned relative to the material CR so that the material CR emits, by interaction of the material CR with the beam 3 of incident particles, one or more beams 4 of diffracted particles (s).
• the beam 3 may be or include an X-ray beam, or an electron beam, or the like.
• the diffracted beam 4 may also correspond to a Kossel type diffraction, a Laue-type diffraction or a diffraction in a transmission electron microscope (in particular diffraction TKD, which is the abbreviation in English of "Transmission Kikuchi Diffraction", diffraction Kikuchi in transmission, carried out in a transmission electron microscope).
• the detector is positioned with respect to the source 2, the beam 3 of incident particles and the material CR, to receive or intercept the beam or beams 4 of diffracted particles (s), derived from the material CR in response to the beam 3 of incident particles .
• the detector 10 comprises, for example, a screen 11 for receiving the beam (s) 4 of diffracted particles.
• the reception screen 11 has a determined extent, for example two-dimensional and flat, or other.
• the reception screen 11 is connected to an image recording / production unit 12 /, g (which may be an automatic calculation unit 12) from the beam (s) 4 of diffracted particles, received or intercepted by the receiving screen.
• the incident particle beam 3 may be or contain incident monochromatic radiation of a given wavelength or several incident monochromatic rays of different determined wavelengths.
• the detector 10 may for example be part of an electron microscope, in particular a transmission and / or scanning electron microscope.
• the screen 11 may be for example a phosphorescent screen, or other.
• the phenomenon of diffraction of the beam 3 of incident particles by the material CR gives rise to the detector 10 to a Laue diagram in the case where the beam 3 of incident particles is a ray beam X, and a Kikuchi image in the case where the beam 3 of incident particles is an electron beam.
• the incident monochromatic radiation 3 of wavelength 1 will diffract on the crystalline planes hk1 (or diffracting planes hkl) of the material CR by respecting:
• n is the diffraction order and d h u the inter-reticular distance of the hkl planes.
• the angle Q is the half-angle between the incident beam 3 and the diffracted beam 4.
• a CR crystalline material whose elementary cell is described by the reference (a, b, c) has a reciprocal lattice whose reference is (a *, b *, c *).
• the Bragg condition can be expressed by the condition of coincidence between the vector q (M /) of the family of crystalline planes hkl, and the diffraction vector q. Only a few favorable directions give rise to a coherent diffraction.
• the electron beam adopted in EBSD has a very low wavelength ⁇ and Q is generally less than 2 ° .
• the electrons under diffraction conditions therefore remain close to the trace of the crystalline plane 40 on which they diffract, as shown in FIG.
• the diffracted beams 4 are distributed on two Kossel CO cones symmetrically with respect to the trace of the crystalline plane 40.
• the cones of Kossel CO sensed by the detector 10 may have a shape of two hyperbolas extremely open, as shown in Figure 1.
• the first image / of the reference state and the second image g of the deformed state are obtained during a single acquisition by scanning the surface of a sample of the material CR .
• the reference state is then taken from the center of the grain (assumed to be the least constrained) which is then compared with diffraction patterns acquired at the periphery of the grain.
• a center O corresponding to the normal projection, in the image plane 110 of the screen 11 of the detector 10, of a source point S of the diffracted beam 4 in the material CR has two predetermined coordinates (x *, y *) in the plane 110 of the screen 11.
• the projection of the beam (s) difffacted (s) 4 on the detector 10 is illustrated in an example non-limiting to Figures 2 and 3.
• the detector 10 is chosen as a reference throughout the suite.
• the bottom left corner B of the plane screen 11 is considered as origin
• the x axis is the horizontal axis in the plane of the screen 110
• the y axis is the vertical axis in the plane of the screen 110
• the axis z is the normal axis to the plane of the screen 110.
• the incident electron beam 3 is directed on the test specimen
• the projection center O is the normal projection (relative to in the plane of the screen 11) of the point S on the plane 110 of the screen 11. Its coordinates are noted (x *, y *, 0). We denote by z * the distance between the source point S and the center O, so S has for coordinates (x *, y *, z *).
• F is denoted by a strain gradient tensor according to the equation below, which, applied to a current point X in the initial configuration of the reference material CR, makes it possible to obtain its position x in the deformed configuration:
• FIG. 1 represents the diffraction of the beam in the microscope chamber, projected onto the screen of the EBSD camera, represented for two crystalline states and the associated gradient gradient tensor for to move from one state to another.
• Figure 3 details the projection, and represents the source point S and the projection center.
• the deformation gradient tensor F is the product of two parts: the elastic part F e (elastic deformation gradient tensor) and the plastic part F p according to the following equation:
• the plastic deformation has the effect of making the Kikuchi strips less clear, an effect difficult to quantify and which does not allow the measurement of the plastic deformation by the analysis of images of diffraction.
• hydrostatic elastic deformation a variation of the width of the Kikuchi bands on the detector is observed.
• the deviatoric elastic deformation changes the shape of the crystalline mesh, ie. the relative orientation of the crystalline planes, so the angular relationships inside the crystal. Projection on a screen far from the source amplifies the angular difference between two beams and gives rise to a measurable variation between the images.
• F e since only eight components of F e are measurable, a convention defining this missing degree of freedom must be defined. According to one embodiment, it is chosen only tensor F having eight components F x, F 2, F, F 4, F 5, F 6, F 7, F ⁇ e t a ninth component set at 1, namely according to equation below:
• the true elastic deformation gradient is then according to the equation below:
• the factor dz / dZ is not measurable but can be determined by additional assumptions (such as the choice of a plane stress state that is often adopted).
• the diffracted ray 4 initially in the direction p is redirected towards the point P ", as
• a displacement function giving the displacement field (u x , u y ) for moving (or "advancing" or matching) the pixels of the first image / to the pixels of a deformed image g, as a function of:
• each of the pixels or “the pixels” may be replaced by “pixels” to designate a portion of the pixels of the image.
• the displacement field (u x , u y ) is equal to, according to equations (9) below:
• the displacement field (u x , u y ) between the first diffraction image /, called the reference image, and the second diffraction image g, called the deformed image, reflects the elastic deformation of the crystalline mesh of the CR material at the studied point. .
• This algorithm is described below for calculating the tensor F elastic deformation gradient. This algorithm may for example be iterative on the steps E7, E8, E9, E10 and E1 described below, as shown in FIG. 4.
• the image processing method is executed by the automatic calculation unit 12, such as for example one or more computer (s) and / or one or more computer (s), and / or one or more processor (s). and / or one or more server (s) and / or one or more machine (s), which can be programmed in advance by a prerecorded computer program.
• the automatic calculation unit 12 such as for example one or more computer (s) and / or one or more computer (s), and / or one or more processor (s). and / or one or more server (s) and / or one or more machine (s), which can be programmed in advance by a prerecorded computer program.
• the tensor F of the current elastic deformation gradient is made to take a determined value F of the elastic strain gradient tensor, such as for example an initial value INIT before the first iteration.
• this initial value INIT before the first iteration can be for example the identity tensor.
• step E7 the current displacement field (u x , u y ) is calculated by applying the function of tensor-dependent displacement F elastic deformation gradient current at both x, y coordinates for each of the pixels of the first image /
• the current displacement field induced by the current elastic deformation gradient tensor at the pixel coordinates of the first image .
• the current displacement field (u x , u y ) is thus calculated as a function of the tensor F current elastic deformation gradient and the coordinates for each of the pixels of the first image during the second calculation step E8.
• the overall digital image correlation consists in correlating the two images / and g.
• the method implements an integrated digital image correlation (abbreviated to CINI).
• CINI integrated digital image correlation
• the method according to the invention can be called abbreviated ADDICTED for Alternative Dedicated Digital Image Correlation Tailored to Electronic Diffraction, or in French alternative digital image correlation, dedicated and adapted to electronic diffraction.
• the image processing method according to the invention can therefore be a method for correcting the second image (s) g and the image processing device according to the invention can therefore be a correction device.
• the second image (s) g can therefore be a method for correcting the second image (s) g and the image processing device according to the invention can therefore be a correction device.
• the displacement fields (u x , u y ) are searched for as linear combinations (or affine) of fields constituting a "kinematic base". They are likely to have any support and then require a global treatment of all kinematics. If in addition said kinematic base is derived from a physical model, and therefore restricted to well-identified mechanisms having a signature in field of displacement, then it will be said "integrated”. The resultant digital image correlation is then also referred to as integrated.
• the CINI is the tool chosen to analyze the diffraction patterns (/ ' and g are the respective diffraction patterns of the crystalline CR or polycrystalline reference material (free of stress for the image f) and the observed crystal (for the image g)
• the manner in which the displacement field (u x , u y ) observed in the diffraction pattern depends here on the elastic deformation is explained.
• other parameters, P can influence the displacement field (u x , u y ) measured, for example projection parameters P, such as the inclination of the specimen with respect to the sensor. 10, the physical size of a pixel and the scanning pitch of the scanning electron microscope, the latter two being summarized by the term beam-induced shift.
• the displacement field (u x , u y ) is explained according to the following equation:
• F corresponds to the sensitivity field in relation to the component (For i ranging for example from 1 to 8) of the gradient tensor F ⁇ j c deformation, and T, is the sensitivity field with respect to the parameter P ;.
• F is a size matrix (2N pixei ) x 8.
• the field of sensitivity of the displacement field u (x) has as components the components and F. (x, F) based on j ec ucitions su 1 veintes!
• the iterative algorithm is Gauss-Newton type. We seek, for example, to minimize the cost function A iteratively by a Gauss-Newton algorithm.
• step E8 the calculation is made q Ui is the third digital pixel value of the corrected distorted image.
• step E8 after step E7 the calculation is made
• a correction vector FJ is calculated that satisfies the following equation:
• step E9 where [M] is a Hessian matrix of dimension 8 ⁇ 8.
• x represents the two x and y coordinates of the pixels.
• the sensitivity field is the sensitivity field of the displacement field (u x , u y ) with respect to the component F ⁇ of the tensor F elastic deformation gradient and is equal to the partial derivative of the displacement field (u x , u y ) relative to to each component F ⁇ of the tensor F elastic deformation gradient.
• the sensitivity field is therefore a two-dimensional vector, which has a component in x, equal to O x - (x; F) and a component in j , equal to O / (x; F e ).
• ⁇ y ⁇ is the second member of the Newton-Raphson method and is the residue vector with components
• V / (x) is the gradient of / fx), that is dc /(.rv).
• step E9 the coefficients are calculated the second member ⁇ y ⁇ according to the following equation:
• the criterion of convergence on the determined value F of tensor being that the norm of the vector the correction value that has been calculated is less than the prescribed positive terminal d e , which is not zero.
• step El 1 after step E10, it is examined after each iteration of steps E7, E8, E9 and E10, if the norm of the vector correction is less than a prescribed positive terminal d e , not zero.
• the terminal of e may be 10 7 or others.
• the updating step E12 described hereinafter is carried out. below.
• the current tensor elastic strain gradient tensor is made to take a determined value tensor.
• the determined value tensor is incremented by the vector FF of correction, according to the equation of updating the determined value
• Step E12 is followed by the first step E7 of calculating the next iteration.
• step E13 in the case where the norm SF 'correction vector having been calculated is less than the prescribed positive terminal d e (case YES of Figure 4), we execute step E13 described below.
• step E13 the determined values of the tensor F elastic deformation gradient calculated during step E12 of the last iteration, which is that verifying the convergence criterion, are retained.
• the displacement field (u x , u y ) calculated during the last step E7 which is calculated by the displacement field (u x , u y ) corresponding to these determined tensor values F s having been retained.
• an output is provided (which can be for example a display on a screen, and / or a recording in a memory, and / or the sending on a port of exit or others) one or more of:
• the corrected image or corrected deformed image g u corresponding to the deformed image g, having been corrected by the corresponding displacement field (u x , u y ), calculated in step E8 as fulfilling the convergence criterion on the determined value F of the elastic strain gradient tensor, that is to say the third digital pixel values having been calculated from the field of displacement (u x , u y ) corresponding, calculated as fulfilling the convergence criterion on the determined value F of the elastic strain gradient tensor,
• a residual field r calculated as the difference between, on the one hand, the third digital pixel values of the corrected distorted image g u , having been calculated for the corresponding displacement field (u x , u y ) as filling the convergence criterion on the determined value F of the elastic strain gradient tensor, and on the other hand the first numerical values flx, y) of pixels of the reference image f
• the method is performed for the most part (for example at least 50%, at least 60%, at least 70%, at least 80% or at least 90% of the pixels of the first image / and the second image g) or all the pixels of the first image / and the second image g, and this at one time for each image.
• the method is executed for several second images g.
• the residual field r collects all the artifacts of the formation and the acquisition of the images, and thus potentially contains very rich information of the analyzed images. Signals in the residue that are not white noise often indicate incomplete information processing or a non-adapted kinematic-to-image transformation model. The residue can therefore contain a signal but also white noise. If it is assumed that the reference image / is formed from a perfect reference image f v without noise, superimposed on a noise b f supposed of normal distribution, without spatial correlation, and well known under the term of "Gaussian white noise": then the image / is equal to, according to the following equation:
• the same reference image is used within the same grain, which therefore corresponds to a single image f but a multitude of images g. It is then observed that the convergence residues obtained for all the images g, can be averaged and, by noting the this average on the different measurement points within a grain, the average of the residues r is equal to, according to the following equations:
• the average of the residues r provides an estimate of the noise ⁇ f , and the noise b t thus calculated is subtracted from the reference image f v . This makes it possible to reduce the measurement uncertainties by decreasing the residue (variance divided by two).
• step E5 the pixel values fx, v) of the first image / and the pixel values g (pc, ⁇ ) of the second image g by a Gaussian filter.
• Gaussian smoothing of the diffraction image on a very small scale makes the subsequent calculation much easier, since the raw image is corrupted by a very large white noise.
• This Gaussian smoothing is to convolute the initial image / (and possibly g) by an emollient function, G
• G (x, y) is chosen as a Gaussian, depending on an internal length x, and which is written:
• the chosen length x may be from 1 to 2 pixels. This choice depends on the noise level on the image, itself a function of the acquisition time, the number of pixels, the beam parameters, the imaged material. Gaussian smoothing effectively eliminates high frequency noise from the diffraction pattern.
• step E4 the pixel values flx, y) of the first image / and the pixel values g (x, y) of the second image g by filtering overexposed pixel values by replacing them with an average of neighboring pixels thereof.
• the acquired images f g often have overexposed pixels at fixed points. These very bright pixels are harmful to the image correlation calculation and it is recommended to replace the gray level value of these "bad pixels" with the average gray level of the neighbors.
• step E4 the pixel values flx, y) of the first image / and the pixel values g (x, y) of the second image g by filtering these pixel values by subtracting global gray scale trends, represented by a second or third order polynomial obtained by a regression process.
• the images / and g may have global variations in gray levels related to fluctuations in the average energy diffracted. For global image correlation, it is preferable in this case to subtract the global greyscale trends.
• step E3 during step E3 preceding step E4, subtracted from the values of pixels f ⁇ x, y) of the first image / and pixel values g (pc, y) of the second image g an image background, having been calculated.
• the images acquired / and g can be tainted with a background due in particular to the energy distribution of the diffracted electrons.
• This background subtraction correction eliminates the average intensity variations of the image, which then increases the contrast and makes the Kikuchi tapes sharper.
• a low-magnification acquisition of crystalline or polycrystalline CR material is carried out in order to scan a large number of grains of different orientations.
• the diffraction images thus acquired are averaged and an estimate of the background can be obtained.
• the background image is unique for the entire study area of an HR-EBSD acquisition.
• Step E2 may be preceded by an input step E1 to input Kikuchi images, center O and parameters P.
• Step E13 may be followed by a post-processing step, for example to obtain other quantities calculated from the quantities obtained in step E13, such as for example a deformation component in the y direction, or others.
• the image processing device 1 of a crystalline or polycrystalline material according to the invention comprises means for implementing the image processing device 1 according to the invention.
• the image processing device 1 according to the invention comprises the diffraction detector 10 making it possible to acquire:
• one or more second image g of the material being in a state that is deformed with respect to the reference state the second image giving second digital values g (pc, ⁇ ) of pixels as a function of the coordinates (pc, y) of the pixels.
• the image processing device 1 comprises at least one computer 12, comprising at least one memory, in which a field (u x , u y ) of moving, to move the pixels of the first image to the pixels of a distorted image, based on:
• predetermined coordinates (e *, y *) of the center O corresponding to the normal projection, in the image plane of the detector, of the source point S of the beam diffracted in the material
• the computer 12 is configured to:
• a third calculation step E8 calculating third digital pixel values of a deformed image g u (x) by correcting the second image g at the pixel coordinates of the displacement field (u x , u y ) current,
• the invention also relates to a computer program, comprising code instructions for implementing the image processing method of a crystalline or polycrystalline material according to the invention, when it is executed on a computer.
• the computer program is stored in a memory of the computer 12.
• the first and second images / and g are obtained after correction of an overall translation of the images by interpolation of the images, according to the following equation of the corrected images f and g:
• the first and second images / and g are obtained after correction by centering at the center O projection.
• the test piece CR material
• the screen 110 can also be disoriented by a few degrees as well. If the acquisition is performed over a large area, the distance z between the transmitting point S and the screen may vary.
• the first image / in the reference state and the second image g in the deformed state of a specimen were made.
• the coarse grained grade AISI 316L stainless steel test piece was polished and tensile loaded inside the chamber of a scanning electron microscope using an in-situ test plate.
• the loading direction is horizontal in FIGS. 5A and 5B.
• an HR-EBSD acquisition was made by considering an area of interest focused on a triple point of the microstructure, that is to say separating three grains G1, G2 and G3.
• the algorithm according to the invention has been used to process the data.
• FIG. 5A shows in an area of interest of the specimen a secondary electron image taken with a scanning electron microscope.
• FIG. 5B shows in the area of interest of the test piece of FIG. 5A an inverse pole figure obtained by standard EBSD analysis.
• FIG. 6A shows the image / reference obtained at a point of the zone of interest, as a function of the coordinates in the plane of the detector, x in the abscissa and y in the ordinates.
• FIG. 6B shows the second image g of the deformed state, as a function of the x coordinates on the abscissa and the y coordinates on the ordinate.
• FIG. 6C shows the initial difference ECI between the image of FIG. 6B and the image of FIG.
• FIG. 6A shows the tensor F elastic deformation gradient, obtained by the ADDICTED method according to the invention from the images / and g of FIGS. 6A and 6B.
• FIG. 6E shows, according to the ECH scale of gray levels represented on the right, the numerical value of the component u x of the displacement field having been calculated from the images of FIGS. 6A and 6B by the ADDICTED method according to the invention, in function of x coordinates on the abscissa and y coordinates on the ordinate.
• FIG. 6D shows the tensor F elastic deformation gradient, obtained by the ADDICTED method according to the invention from the images / and g of FIGS. 6A and 6B.
• FIG. 6E shows, according to the ECH scale of gray levels represented on the right, the numerical value of the component u x of the displacement field having been calculated from the images of FIGS. 6A and 6B by the ADDICTED method according to the invention, in function of x coordinates on the abscis
• FIG. 6F shows, according to the ECH scale of gray levels (numerical values of pixels) represented on the right, the numerical value of the other component u y of the displacement field having been calculated from the images of FIGS. 6A and 6B by the ADDICTED method according to the invention, as a function of the x coordinates on the abscissa and the coordinates y on the ordinates.
• FIG. 6G shows the deformed and corrected image g u , that is to say having been corrected from FIG. 6B by the displacement field (u x , u y ) of FIGS. 6E and 6F, having been calculated from the images of FIGS.
• FIG. 6H shows the residual field r, equal to the difference between the corrected deformed image g u of FIG. 6G, obtained by the method
• Fig. 61 shows a G3 grain diffraction image, where the signals contained in the 6H image are visible.
• FIG. 6C There is a rotation that is not very visible to the naked eye between the two images of FIGS. 6A and 6B, but is noticeable when calculating the initial difference between them, as illustrated in FIG. 6C. It can be concluded from FIGS. 6H and 6C that the dominant initial deviation illustrated in FIG. 6C disappears thanks to the ADDICTED method according to the invention in FIG. 6H and that a "ghost" band field becomes visible in the residues of FIG. Figure 6H.
• the identity matrix is a good choice for the tensor F s because of the small expected deformations, and the absence of additional information.
• Fe 4 obtained is less than 10.
• V e l + £
• the components s cc , s gg , s cg , s gz and s cz of the stress tensor obtained by the ADDICTED method according to the invention are respectively represented in FIGS. 7A, 7B, 7C, 7D and 7E as a function of the coordinates x in abscissa and coordinates y on the ordinate.
• the s zz component of the stress tensor obtained by the ADDICTED method according to the invention is too weak to be distinguished from 0 and is therefore not represented.
• FIG. 8A The equivalent von Mises stress obtained by the ADDICTED method according to the invention is represented in FIG. 8A according to the gray scale ECH shown on the right, as a function of the x coordinates on the abscissa and the y coordinates on the ordinate.
• Figure 8B shows a histogram of the equivalent von Mises stress of Figure 8A.
• the extreme von Mises stress value is 2.7 GPa for the ADDICTED method according to the invention.
• the automatic execution of the method according to the invention, for Matlab coded programming takes 40 hours on a laptop using two i7 cores.
• the CrossCourt program takes about 40 hours for the first calculation only, and 100 hours with the reframing ("remapping", above).
• the method according to the invention thus drastically reduces (by 75% or 90%) the calculation time with programming in interpreted language, which uses a non-compiled and non-optimized code.
• the invention makes it possible to measure the deformations and to evaluate the constraints precisely.
• the invention has the following advantages:
• the pre-rotation operation is intrinsically incorporated into the resolution by the ADDICTED method according to the invention.
• the global correlation strategy according to the invention also makes it possible to avoid redundancy in the calculations carried out (where the inter-correlation method of the state of the art of the technique generates overlaps of the images) and therefore of to gain considerable computing time (from 75% to 90% depending on the test case).
• the global correlation strategy reduces measurement uncertainty, a reduction of 40% has been highlighted in a simple interpretation test case.
• the strategy takes a wide and unique area of interest, ie. it samples a large number of pixels at one time.
• the ADDICTED method according to the invention is optimal with respect to a Gaussian white noise affecting the diffraction images.
• improvements have been proposed, such as for example the application of a Gaussian smoothing in the diffraction pattern to attenuate the high frequency noise, or the initialization of the calculation by the results of neighboring elements. .
• the field of correlation residues is intrinsically obtained by the process according to the invention, whereas it is not calculated by state-of-the-art techniques and is expensive to manufacture. calculate when you want to get it by these techniques, because it would require a lot of interpolations.
• calculate when you want to get it by these techniques, because it would require a lot of interpolations.
• by analyzing the residuals of all the calculations one can "denoise" all the Kikuchi images, or detect any errors existing in the background noise.
• the ADDICTED method according to the invention adapted to HR-EBSD images, can be extended to other types of diffraction-obtained images, for example Kossel diffraction, Laue diffraction or TEM diffraction (transmission electron microscope). ). These techniques are based on the same principle of projection of diffracted beams.
• the ADDICTED method according to the invention can be focused on these techniques.
• the ADDICTED method according to the invention for diffraction Laue and MET brings significant gains on their exploitation.
• the above embodiments, features and examples may be combined with each other or selected independently of one another.

Landscapes

• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Engineering & Computer Science (AREA)
• Chemical & Material Sciences (AREA)
• Life Sciences & Earth Sciences (AREA)
• Analytical Chemistry (AREA)
• Biochemistry (AREA)
• General Health & Medical Sciences (AREA)
• Health & Medical Sciences (AREA)
• Immunology (AREA)
• Pathology (AREA)
• Theoretical Computer Science (AREA)
• Crystallography & Structural Chemistry (AREA)
• Quality & Reliability (AREA)
• Computer Vision & Pattern Recognition (AREA)
• Analysing Materials By The Use Of Radiation (AREA)
• Image Processing (AREA)

Applications Claiming Priority (2)

Publications (3)

Family

ID=61913276

Family Applications (1)

Country Status (6)

Families Citing this family (6)

Family Cites Families (40)

• 2017
  • 2017-12-11 FR FR1761926A patent/FR3074949B1/fr active Active
• 2018
  • 2018-12-07 WO PCT/EP2018/083947 patent/WO2019115381A1/fr unknown
  • 2018-12-07 US US16/771,415 patent/US11526980B2/en active Active
  • 2018-12-07 EP EP18811580.2A patent/EP3724646B8/de active Active
  • 2018-12-07 CN CN201880089066.9A patent/CN111699380B/zh active Active
  • 2018-12-07 ES ES18811580T patent/ES2910109T3/es active Active

Also Published As

Similar Documents

Legal Events